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\author{五六七 }
\title{运动员参赛策略 }

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\begin{document}

\maketitle

\begin{abstract}
使用非合作的双矩阵博弈的混合策略，为本队运动员制定最佳参赛方案。
\end{abstract}

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\section{问题描述}
有甲乙两支游泳队举行对抗赛，对抗赛一共有三个项目，分为蝶泳、仰泳和蛙泳。
这两支游泳队里，各有一名健将，甲队为李，乙队为王，他们在三个项目中的成绩都很突出。
但是竞赛规则准许他们每人只能参加两项比赛，而其他运动员可以参加全部三项比赛。
已知所有运动员的平时成绩如表所示。

\begin{table}[ht!]\centering
\caption{两队运动员的平时成绩} \vspace{0.2cm}
\begin{tabular}{|M{2.5cm}||M{1.5cm}|M{1.5cm}|M{1.5cm}||M{1.5cm}|M{1.5cm}|M{1.5cm}|}\hline
项目 & 甲队赵  & 甲队钱 & 甲队李 & 乙队王 & 乙队张 & 乙队孙   \\ \hline \hline 
100米蝶泳 & 59.7 & 63.2 & 57.1 & 58.6 & 61.4 & 64.8  \\ \hline 
100米仰泳 & 67.2 & 68.4 & 63.2 & 61.5 & 64.7 & 66.5  \\ \hline 
100米蛙泳 & 74.1 & 75.5 & 70.3 & 72.6 & 73.4 & 76.9  \\ \hline 
\end{tabular}
\end{table}

假设运动员们在比赛中都发挥正常水平。比赛第一名得5分，第二名得3分，第三名得1分。
假设两队的参赛报名情况互相保密，报名后不能变动。
问教练员应该让自己的运动健将（甲队李和乙队王）参加哪两项比赛，使得本队得分最多？



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\section{建立模型}




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\section{编程计算}




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\section{回答问题}




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%\section{参考文献 }
\begin{thebibliography}{99}

%\bibitem{dingtongren} 丁同仁、李承治，常微分方程教程，高等教育出版社，2022年3月第三版。
\bibitem{sishoukui-2} 司守奎,孙玺菁. \emph{Python数学建模算法与应用}, 国防工业出版社. 2022年1月第1版. 
%\bibitem{hexiaoqun-ara} 何晓群. \emph{应用回归分析(R语言版)}. 电子工业出版社. 2017年7月第1版. 
%\bibitem{dalgaard} Peter Dalgaard 著, 郝智恒等译. \emph{R语言统计入门}. 人民邮电出版社. 2014年6月第1版. 


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